Eight-component two-fermion equations

An eight-component formalism is proposed for the relativistic two-fermion problem. In QED it extends the applicability of the Dirac equation with hyperfine interaction to the positronium case. The use of exact relativistic two-body kinematics entails a $\mathrm{CP}$-invariant spectrum that is symmetric in the total center-of-mass system energy. It allows the extension of recent ${\ensuremath{\alpha}}^{6}$ recoil corrections to the positronium case and implies recoil corrections to the fine and hyperfine structures and to the Bethe logarithm.